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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 74r, page id 00068195:0147
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liliter aequationem numerulam in literalem
pro tollendis irrationalibus cogniers ex aequatione; Cartesius
ita procedit ut incognitam radicem multiplicet per quandam
irationalem vig. ii aequatione X - S3 XX + 26, X - 8
Demius radi ce =B3, : B. 4 B
27B
sive s 3 Xx + 26 (3X 83 ponites y aequ X 13. unde fit
9y - 3kg. - 39y +26y F8 aq. 0. multiplicando terminum
secundum per prioris per 13. et tertium per quadrulum ejus 3 et
quartum per cubum ejus 3 13.
Sed qusi fuisset aequatio
X - S3 XX + 3B X = 8 aeq. 0. non processisset artific
cium. Quid ergo tunc agemus? an exaltabimus aequationem ad alhorem
gradum, faciendo Xt3 aequ X X - 8, : c3 - X. unde fiet.
3X aequ  X - 3X 1bX + 190 264, : X = bX + 9  et
tandem X - 3X + 2X = 27 X + 64, aq. 0.
s
Hcdem ita procedunt, sed praestaret hanc aequalionem posse vitare
quod ita quem in finem tate artificdium commentus sum, unitas servetur
in literam servuta lege homogeneorum sict X at X +3 aa B X - ea
An ad sciendum an procedat dvisco satis erit quod si pro numeris
adhibeamus hiteras scrvata leger homo geneorum, nemper pro S3
scribendo b, et pro 1 scribendo a. vel a vel a pro ut opus est fiet
X = b x + 3ab X = ga aeq. ob  abi + supponendo 3aa aequbt
possumus scribere: X- b X + 3 ab X = 8 a aq. 0.
nam ad aequationem impunese
+3faa  439 4
=F bb
=
ab
possumus addere  id quod valet nihil. P. +3hab
at hoc est egregium artificium mutandi Rumeratem in
3aa - bb aey.
9a + hb
34 a galb
o0q. 39a- g abb + 3 haab. s
literatem se vata lege homogeneorum (nam f. h. g non sunt revera
Uterae sed numeri arbitrarii) et ita ut variae habitudines quibus
eadem quantitas numeralis posset mutari in lileralem adhibitis arbitrams
sumul comprehendantur. En si Ac si videndum jam est an arbitrariae
ita exali assumi possint, ut succedat divisio per X + Ia + m b
qut
esumta prima aequatione  senbendo pro X scrbendo 53, b. eit 3 aequ bb
et 27 aa aequ 16 aet sint
b
mumi f v prpr b vita rebilti a
X + = b a X = 8a vel pro X
bu da. scd. W. 11 a fi v db a1 
sperte